Ross Barkley, Pedro, Cesc Fabregas, Tiemoue Bakayoko Marcos Alonso and David Luiz were among the big names to have returned.
Chelsea travel to Western Australia to take on Perth Glory in a friendly on July 23, before participating in the International Champions Cup with fixtures against Inter, Arsenal and Lyon either side of facing Premier League champions Manchester City in the Community Shield on August 5.
And Sarri's presence in London could yet give Chelsea the edge in the race.
The Italian has been widely tipped to leave Stamford Bridge this summer following a disappointing campaign which saw Chelsea finish fifth in the Premier League, although they did end the season with FA Cup glory.
The managerial saga has dragged on and on over the course of the summer, with Chelsea players left in confusion having already returned to their Cobham training ground for pre-season training.
Meanwhile, Chelsea are struggling to agree a compensation package with current manager Antonio Conte - who is said to have been absent from training at Cobham this week.
Fellow Italian Maurizio Sarri has been the main man in the frame to succeed his fellow countryman, although Sky Sports Italy have reported that negotiations between Napoli and Chelsea regarding Sarri's appointment as Conte's potential replacement are in 'deadlock'.
An agreement in principle is in place to bring Sarri to Stamford Bridge, but the Blues still need to work with Napoli to secure his release from his contract.
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